OK. So not a resonant circuit. just a controlled relay.
Looking at the schematic, C1 looks like it's serving as a filter cap. When Q1 fires, the 150 VDC will (should) supply the power to energize the relay coil, i.e., the cap won't discharge much of a discernible current. Of course, when the 150 VDC is removed (at power down, or whatever), then C1 will discharge eventually, but since we don't know what sort of bleeder resistors may be in the power supply circuitry, the time constant isn't known.
That said, if the 0.5 ohm resistor is connected to an actual ground (not floating) then your ground test lead hookup looks fine.
I might add, though, that it's unlikely that you'll see much of a voltage presence across R1 except at the initial application of power as the cap charges up to the 150 VDC limit.